Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$(\frac{x^{\prime}}{x^{m}})^{1+m}\times\frac{(x^{m}}{x^{n}})^{m+n}\times\frac{(x^{n}}{x!})^{n+1}$$

Answer

$$x^(p+m)*r*m*IM*e+m*x^((m+n)*m)+n*x^n^2*x!^n+1$$

Solution


Regroup terms.
\[{({x}^{p}{x}^{m}rm\imath e)}^{1}+m{({x}^{m}{x}^{n})}^{m}+n{({x}^{n}x!)}^{n}+1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{({x}^{p+m}rm\imath e)}^{1}+m{({x}^{m}{x}^{n})}^{m}+n{({x}^{n}x!)}^{n}+1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{({x}^{p+m}rm\imath e)}^{1}+m{({x}^{m+n})}^{m}+n{({x}^{n}x!)}^{n}+1\]
Use Rule of One: \({x}^{1}=x\).
\[{x}^{p+m}rm\imath e+m{({x}^{m+n})}^{m}+n{({x}^{n}x!)}^{n}+1\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{x}^{p+m}rm\imath e+m{x}^{(m+n)m}+n{({x}^{n}x!)}^{n}+1\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[{x}^{p+m}rm\imath e+m{x}^{(m+n)m}+n{({x}^{n})}^{n}{x!}^{n}+1\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[{x}^{p+m}rm\imath e+m{x}^{(m+n)m}+n{x}^{nn}{x!}^{n}+1\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{x}^{p+m}rm\imath e+m{x}^{(m+n)m}+n{x}^{{n}^{2}}{x!}^{n}+1\]
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